Benitez and the Portuguese coach had made little secret of their animosity over the last few years, heightened by run-ins over Champions League semi-finals and his frequent comments that it was Roman Abramovich's billions that bought back-to-back Premier League titles for the west Londoners.
Even though Sir Alex Ferguson and Arsene Wenger of the 'big four' have offered their sympathies for his departure, all Benitez would say was: "You know my relationship with him, it is better that I do not say anything.
"At the moment I am more worried about Birmingham boss Steve Bruce."
Liverpool face the Midlanders at Anfield on Saturday.
Benitez said: "It is not a good idea for a manager to talk about other clubs in this situation.
"I would prefer not to say anything. What is clear is that Chelsea still have a good team with a lot of very good players."
He added: "The best thing for Liverpool is to continue to focus on what we are doing and to continue to improve ourselves and play well. Not to think about what is happening anywhere else.
"That would be dangerous, I am more interested in Liverpool, not with any problems at other clubs."